Rising carbon dioxide (CO2) concentrations in the atmosphere result in increasing global temperatures and ocean warming (OW). Concomitantly, dissolution of anthropogenic CO2 declines seawater pH, resulting in ocean acidification (OA) and altering marine chemical environments. The marine biological carbon pump driven by marine photosynthesis plays an important role for oceanic carbon sinks. Therefore, how ocean climate changes affect the amount of carbon fixation by primary producers is closely related to future ocean carbon uptake. OA may upregulate metabolic pathways in phytoplankton, such as upregulating ß-oxidation and the tricarboxylic acid cycle, resulting in increased accumulation of toxic phenolic compounds. Ocean warming decreases global phytoplankton productivity; however, regionally, it may stimulate primary productivity and change phytoplankton community composition, due to different physical and chemical environmental requirements of species. It is still controversial how OA and OW interactively affect marine carbon fixation by photosynthetic organisms. OA impairs the process of calcification in calcifying phytoplankton and aggravate ultraviolet (UV)-induced harms to the cells. Increasing temperatures enhance the activity of cellular repair mechanisms, which mitigates UV-induced damage. The effects of OA, warming, enhanced exposure to UV-B as well as the interactions of these environmental stress factors on phytoplankton productivity and community composition, are discussed in this review.